Definition:Adjacent (Graph Theory)/Vertices/Undirected Graph

Definition

Let $G = \struct {V, E}$ be an undirected graph.

Two vertices $u, v \in V$ of $G$ are adjacent if and only if there exists an edge $e = \set {u, v} \in E$ of $G$ to which they are both incident.

Otherwise they are non-adjacent.

Also known as

Adjacent elements of a graph can also be described as neighboring (British English spelling: neighbouring).

Also see

• Results about adjacency in the context of graph theory can be found here.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs